Uma proposta de ensino de continuidade de funções em cálculo diferencial e integral a partir da noção de complementaridade

Abstract

This scientific production is a qualitative, bibliographic and explanatory research to obtain a Master's degree at the Postgraduate Program in Mathematics Education at the Federal University of Juiz de Fora — UFJF. With this work we propose to present the considerations of our Master's research, which aims to investigate the processes of visualization, semiotic representations, and production of meanings in the context of the training of math teachers, especially focused on the concept of continuity. For this intent, we propose as a starting point the analysis of different notions of the concept of continuity, how it has been applied and studied over time by different authors, and how each of them indicates the importance of using intuition. We adopted Peirce's Semiotics and Otte's complementarity as a theoretical basis and sought possible relationships between Mathematics Education, the theoretical aspects of Peircean Semiotics mediation, and the application of thought experiments to understand the idea of continuity by means of an approach through the complementarity between intuition and concept; intuition and logic, using the thoughts of Poncelet and Cauchy. One of the objects of this research was the production of a set of tasks that would help in the development of the concept of continuity. And as a goal, we made an educational product which consists of a sequence of activities elaborated to help in the training of mathematics teachers and that can also be adapted for application to calculus students.